Quantifying displacement: an urban expansion consequence via persistent homology
A novel method applies persistent homology to public address data, revealing hidden displacement patterns in cities.
Researchers Rita Rodríguez Vázquez and Manuel Cuerno have published a novel paper titled 'Quantifying displacement: an urban expansion consequence via persistent homology' on arXiv. The work addresses a critical gap in urban studies: reliably measuring long-term, involuntary residential displacement caused by economic change and housing pressures. Traditional methods struggle because displacement is a gradual process that can't be captured in single data snapshots and is hard to compare across different cities.
Their solution is a computational geometry tool that applies Topological Data Analysis (TDA), specifically persistent homology, to publicly available address-change data. The method constructs four-dimensional 'cubical complexes' that simultaneously incorporate geographical and temporal information about population movement over extended periods. In a 20-year case study of Madrid, Spain, the tool successfully identified which specific neighborhoods experienced displacement and during which years, revealing patterns completely obscured in the raw address data. This provides urban planners and policymakers with a powerful, replicable framework to objectively assess the social consequences of urban transformation.
- Novel method uses Topological Data Analysis (TDA) and persistent homology to model displacement as a gradual, spatiotemporal process.
- Constructs 4D 'cubical complexes' from public address data to track movement geography and time simultaneously over long spans.
- 20-year Madrid case study proved the tool identifies affected neighborhoods and years, revealing patterns invisible in raw data.
Why It Matters
Provides urban planners a replicable, data-driven tool to objectively measure the human cost of gentrification and urban expansion over decades.